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Discovery Algorithms for Hierarchical Relations

Published online by Cambridge University Press:  01 January 2025

Lewis C. Price ,
C. Mitchell Dayton  and
George B. Macready
Lewis C. Price*
Affiliation:
Macro Systems, Inc.
C. Mitchell Dayton
Affiliation:
University of Maryland
George B. Macready
Affiliation:
University of Maryland
*
Requests for reprints should be sent to Lewis C. Price, Macro Systems, Inc., 8630 Fenton Street, Suite 300, Silver Spring, Maryland 20910.
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Abstract

Two algorithms based on a latent class model are presented for discovering hierarchical relations that exist among a set of K dichotomous items. The two algorithms, stepwise forward selection and backward elimination, incorporate statistical criteria for selecting (or deleting) 0-1 response pattern vectors to form the subset of the total possible 2k vectors that uniquely describe the hierarchy. The performances of the algorithms are compared, using computer-constructed data, with those of three competing deterministic approaches based on ordering theory and the calculation of Phi/Phi-max coefficients. The discovery algorithms are also demonstrated on real data sets investigated in the literature.

Keywords

probabilistic modellatent class modelhierarchical relationslatent structure analysisdiscovery algorithms

Information

Type
Original Paper
Information
Psychometrika , Volume 45 , Issue 4 , December 1980 , pp. 449 - 465
Copyright
Copyright © 1980 The Psychometric Society

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References

Reference Notes

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